Abstract
A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. In 1989, it was shown that every connected planar graph with at least 8 vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is 5-connected planar triangulation or 5-connected plane graphs with few non-triangular faces.In this paper, we prove that if G is a 5-connected plane graph of even order in which at most two faces are not triangular and M is a matching of size four in which the edges lie pairwise distance at least three apart, then M is extendable. A related result concerning perfect matching with proscribed edges is shown as well.
| Original language | English |
|---|---|
| Journal | Discrete Mathematics |
| DOIs | |
| Publication status | Accepted/In press - 2017 |
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Keywords
- Distance restricted matching extension
- Plane graph
- Punctured triangulation
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
Cite this
Edge proximity and matching extension in punctured planar triangulations. / Aldred, R. E.L.; Fujisawa, Jun; Saito, Akira.
In: Discrete Mathematics, 2017.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Edge proximity and matching extension in punctured planar triangulations
AU - Aldred, R. E.L.
AU - Fujisawa, Jun
AU - Saito, Akira
PY - 2017
Y1 - 2017
N2 - A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. In 1989, it was shown that every connected planar graph with at least 8 vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is 5-connected planar triangulation or 5-connected plane graphs with few non-triangular faces.In this paper, we prove that if G is a 5-connected plane graph of even order in which at most two faces are not triangular and M is a matching of size four in which the edges lie pairwise distance at least three apart, then M is extendable. A related result concerning perfect matching with proscribed edges is shown as well.
AB - A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. In 1989, it was shown that every connected planar graph with at least 8 vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is 5-connected planar triangulation or 5-connected plane graphs with few non-triangular faces.In this paper, we prove that if G is a 5-connected plane graph of even order in which at most two faces are not triangular and M is a matching of size four in which the edges lie pairwise distance at least three apart, then M is extendable. A related result concerning perfect matching with proscribed edges is shown as well.
KW - Distance restricted matching extension
KW - Plane graph
KW - Punctured triangulation
UR - http://www.scopus.com/inward/record.url?scp=85027441616&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027441616&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2017.07.017
DO - 10.1016/j.disc.2017.07.017
M3 - Article
AN - SCOPUS:85027441616
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
ER -